A Subtle Symmetry of Lebesgue's Measure


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Uludag M. , Ayral H.

JOURNAL OF THEORETICAL PROBABILITY, vol.32, no.1, pp.527-540, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.1007/s10959-017-0804-y
  • Title of Journal : JOURNAL OF THEORETICAL PROBABILITY
  • Page Numbers: pp.527-540

Abstract

We represent the Lebesgue measure on the unit interval as a boundary measure of the Farey tree and show that this representation has a certain symmetry related to the tree automorphism induced by Dyer's outer automorphism of the group PGL(2,Z). Our approach gives rise to three new measures on the unit interval which are possibly of arithmetic significance.